A305175 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 4, 18, 0, 0, 61, 46, 46, 61, 0, 0, 209, 151, 410, 151, 209, 0, 0, 702, 543, 2397, 2397, 543, 702, 0, 0, 2381, 2120, 13970, 26810, 13970, 2120, 2381, 0, 0, 8069, 8155, 93426, 218476, 218476, 93426, 8155, 8069, 0, 0, 27330, 30205, 586718

Offset

1,5

Comments

Table starts

.0....0.....0.......0.........0..........0............0..............0

.0....3.....5......18........61........209..........702...........2381

.0....5.....4......46.......151........543.........2120...........8155

.0...18....46.....410......2397......13970........93426.........586718

.0...61...151....2397.....26810.....218476......2416954.......24233688

.0..209...543...13970....218476....2549718.....40793823......587542013

.0..702..2120...93426...2416954...40793823...1069089450....24206013485

.0.2381..8155..586718..24233688..587542013..24206013485...830801270567

.0.8069.30205.3677924.237639509.8317497391.531063626743.27606232235363

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

k=3: [order 18]

k=4: [order 66] for n>67

Example

Some solutions for n=5 k=4
..0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..0..1..0..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
..0..0..0..1. .1..1..1..0. .0..1..1..1. .0..1..0..1. .0..0..0..0
..0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0. .1..0..1..1
..1..0..1..0. .1..1..1..0. .0..1..1..0. .1..1..0..1. .0..1..0..0

Crossrefs

Column 2 is A303684.

Sequence in context: A303690 A304156 A305509 * A316763 A304065 A305457

Adjacent sequences: A305172 A305173 A305174 * A305176 A305177 A305178

Keyword

nonn,tabl

Author

R. H. Hardin, May 26 2018

Status

approved